Republican presidential candidate, former Texas Gov. Rick Perry speaks at the Defending the American Dream summit hosted by Americans for Prosperity at the Greater Columbus Convention Center in Columbus, Ohio, ... more

Carson, in fact, drew even with Trump in the Monmouth University poll released Monday, marking the first time that a poll in any of the first four nominating states has not shown Trump with a nominal lead.

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Of the top four in the poll, Cruz, the junior U.S. senator from Texas, is the only office holder.The next tier of candidates includes Scott Walker, at 7 percent, Jeb Bush at 5 percent, John Kasich and Marco Rubio at 4 percent each, and Rand Paul at 3 percent.

Although the poll found that the vast majority of voters say their eventual support could go to one of several other candidates, the numbers show Perry going in the wrong direction in Iowa, the first-in-the-nation caucus state.

Perry was lumped in a group of six GOP candidates who registered at 1 percent or less. In a July Monmouth poll – before the first debate in Cleveland – he was at 3 percent.

But Perry is not the only governor, or ex-governor, to fade in the poll. Walker, the Wisconsin governor, was the Iowa leader in the last Monmouth poll in July with 22 percent support.

"These results mark a significant shake-up in the leader-board from Monmouth's Iowa poll taken before the first debate," said Patrick Murray, director of the independent Monmouth University Polling Institute in West Long Branch, N.J. "Carson and, to a lesser extent, Fiorina have surged, while Walker has faded into the background."

If there's any good news for Perry's comeback hopes, it's the finding that only 12 percent of the poll's respondents are completely decided on which candidate they will support in February.

The Monmouth poll was conducted by telephone from August 27 to 30 with 405 Iowa voters likely to attend the Republican presidential caucuses on February 1. The sample has a margin of error of plus or minus 4.9 percent.